## How the tunnel junction excited by a current source

Ans. Fig. 3.5 shows a circuit that leads to a surprisingly complex phenomenon consists of a tunnel junction fed by a constant current source Is For a classical ideal capacitor (where no

tunneling allowed), the relation between voltage and current

The voltage over a current-source driven capacitor will increase linearly with respect to time,

The voltage then decreases by 1qe1C, and the process repeats itself; v as shown in fig. 3.6. The net result C

is that the voltage across the capacitor oscillates, which is known as single-electron tunneling **(SET)** oscillation The period of oscillation can be calculated as

Therefore, the time between tunneling events is on the order of s assuming nanoamp currents which is ·much larger than the typical tunneling time of s.

It turns out that the oscillation is difficult to observe due to experimental’ factors, such as the generally high lead capacitance in experimental systems. To assess this issue, consider the world as see n by the tunnel junction In a circuit model, the tunnel junction is connected to external bias and measurement circuitry by some. lengths of electrical leads. The fact that there is. no direct electrical contact between the-island and the leads is modeled by the tunnel junction itself, via the tunnel res instance Rt and junction capacitance C